A weakly nonlinear model for multi-modal evolution of  wind-generated long internal waves in a closed basin

Sakai, Takahiro; Redekopp, L. G.

doi:10.5194/npg-16-487-2009

Cited by 6 publications

(6 citation statements)

References 20 publications

(27 reference statements)

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Section: Model Descriptionmentioning

confidence: 99%

“…Intermodal coupling can play an important role in the evolution of weakly nonlinear internal waves, particularly second-mode nonlinear internal waves (Shroyer et al, 2010). Therefore, the multi-modal evolution equation set found in Sakai and Redekopp (2009), which contains the derivation of the set from the Euler equations to the final evolution equation set comprising the first and second modes, is used to simulate the evolution of a shoaling IT. Here, we present only the final results of the derivation of this equation set.…”

Section: Model Descriptionmentioning

confidence: 99%

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Generation of second-mode internal solitary waves during winter in the northern South China Sea

Liang

2019

Ocean Dynamics

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Key Points: The evolution of an internal tide mode is examined with intermodal coupling.  A generation mechanism of observed mode-2 internal solitary waves during the winter is presented. A mode-1 internal tide can efficiently scatter into mode-2 waves during the winter.Confidential manuscript submitted to replace this text with name of AGU journal Abstract Field measurements of second-mode internal solitary waves (mode-2 ISWs) during the winter on the upper continental slope of the northern South China Sea were reported in Yang et al. (2009), but their generation mechanism remains elusive. We investigated this issue with a multi-modal evolution model and theoretical analysis, which suggest that the observed mode-2 ISWs were generated by a shoaling mode-2 semidiurnal internal tide (IT) that emanated from the Luzon Strait. The results show that two groups of mode-2 ISWs usually appear within one semidiurnal tidal period, successively riding on expanded and subsequently compressed pycnoclines. The number of wave groups largely depends on the amplitudes of the ITs; that is, a larger IT produces larger mode-2 ISWs. Furthermore, intermodal coupling dominates the evolution of a mode-1 IT, highlighting the importance of considering mode scattering in the propagation of low-mode ITs. solitary-likewaves,

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Section: Model Descriptionmentioning

confidence: 99%

Section: Model Descriptionmentioning

confidence: 99%

Generation of second-mode internal solitary waves during winter in the northern South China Sea

Liang

2019

Ocean Dynamics

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“…With the goal of quantifying the examined situation as illustrated in Fig.1, a generation model that accounts for intermodal interaction is derived based on a multi-modal approach. The multi-modal approach has been successfully used in multiple studies of internal waves, such as development of internal solitary waves in various thermocline regimes [31], internal tide generation at the continental shelf [32] and multi-modal evolution of wind-generated long internal waves in a closed basin [33]. All of the previous works are restricted to a one-dimensional stratification, that is, density is only varying in the vertical direction.…”

Section: Iwsmentioning

confidence: 99%

“…A little difference between Eq. ( 29) and the derived definition of Sakai and Redekopp [33] exists, which lies in the additional consideration of transverse velocity in Eq.…”

Section: Favorable Environmental Condition For Model -2 Iws' Formationmentioning

confidence: 99%

Generation of mode-2 internal waves in a two-dimensional stratification by a mode-1 internal wave

Liang

et al. 2018

Wave Motion

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The generation of mode-2 nonlinear internal waves (IWs) by the evolution of a mode-1 IW in a two-dimensional stratification is investigated. A generation model accounting for intermodal interaction is derived based on a multi-modal approach in a weakly nonlinear and non-hydrostatic configuration. The generation model is numerically solved to simulate the evolution of mode-1 and mode-2 IWs in an inhomogeneous pycnocline. The numerical experiments confirm that a mode-2 IW is generated due to linear and nonlinear intermodal interaction. The mode-2 IW continues growing and gradually separates with the mode-1 IW during the generation process. A non-dimensional quantity quantifying the mode-2 IWs' energy is used to investigate the favorable conditions for the formation of mode-2 IWs. The numerical results suggest that the pycnocline strength or depth prominently affects the formation of mode-2 IWs, followed by pycnocline thickness. A weakening or shoaling pycnocline favors the formation of mode-2 IWs by evidently enhancing linear and nonlinear intermodal interaction, whereas a thinning pycnocline favors the process mainly by enhancing nonlinear intermodal interaction. Shortening the front length inhibits nonlinear intermodal interaction while equivalently strengthens the linear intermodal interaction. Increasing the initial mode-1 IW amplitude can noticeably increase the produced mode-2 IW amplitude.

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“…Such a model, of course, precludes any leakage of energy into higher vertical modes, an effect that almost surely is an important element in the energy transfer to shorter scales in a closed basin, especially for waves propagating through horizontal contractions and undergoing 'reflections' from sloping endwalls. Such effects will be addressed in a subsequent study where coupled-mode evolution equations are derived and simulated (Sakai & Redekopp 2009).…”

Section: Evolution Modelmentioning

confidence: 99%

A parametric study of the generation and degeneration of wind-forced long internal waves in narrow lakes

Sakai

Redekopp

2010

J. Fluid Mech.

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The generation and energy downscaling of wind-forced long internal waves in strongly stratified small-to-medium sized narrow lakes are studied. A two-layer nonlinear model with forcing and damping is employed. Even though the wave field is fundamentally bidirectional in nature, a domain folding technique is employed to simulate the leading-order internal wave field in terms of a weakly nonlinear weakly dispersive model equation of Korteweg–deVries type. Parametric effects of wind-forcing and environmental conditions, including variable topography and variable basin width, are examined. Energy downscaling from basin-scale waves to shorter scales are quantified by means of a time evolution of the wave energy spectra. It is demonstrated that an internal wave resonance is possible when repetitive wind-forcing events arise with a frequency near the linear seiche frequency. An attempt is made to apply the model to describe the shoaling of long waves on sloping endwall boundaries. Modelling of the energy loss and energy reflection during a shoaling event is calibrated against laboratory experiments.

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A weakly nonlinear model for multi-modal evolution of wind-generated long internal waves in a closed basin

Cited by 6 publications

References 20 publications

Generation of second-mode internal solitary waves during winter in the northern South China Sea

Generation of second-mode internal solitary waves during winter in the northern South China Sea

Generation of mode-2 internal waves in a two-dimensional stratification by a mode-1 internal wave

A parametric study of the generation and degeneration of wind-forced long internal waves in narrow lakes

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